Bachelor of Technology [B.Tech] + M.Tech (Engineering Design) From IIT Madras, Chennai

For obvious reasons, ED in IIT Madras is better than EE from IIT Mandi.

Since, you are a Keralite, you need to travel across the entire length of India whenever you need to travel back and forth from your home. Moreover, the climate will also be a minus factor. In case of Chennai, you can travel overnight and reach your home. The people there will be more familiar to you as compared to those in Mandi.

Engineering Design - 

• It is an amalgamation of all the engineering disciplines in a crude sense which can be easily seen by their curriculum. 
• The curriculum includes doing coding, mechanical labs and civil engineering courses, it even includes Electrical Engineering. 
• BTech in Electrical Design is a 5 year Program as it includes a compulsory six month internship (an entire semester) in the final year and a project in the final year of the course. Whereas, the courses at other branches last for only 8 weeks.

To summarize, IIT Madras offers you everything that IIT Mandi has and a lot more than that.

Mandi is situated in Himachal Pradesh, it has a very pleasing scenery. But keeping in mind the distance, weather conditions and the ease of living for a Keralite, Chennai is a much better option.

The choice should be based on your subject of interest. IIT Bhubaneswar is among the newly open IITs, whereas IIT Madras is an oldest and well-established institute.

IIT Madras offers dual degree programs in Engineering Design. It is a very practical course and offers a lot of opportunities. The students with a good GPA can get recruited by core companies. In 2019 placements, students of ED got placed in reputed companies with packages ranging between 7 LPA to 26 LPA. The placement rate of ED was 83%.

The department of Mechanical Engineering in IIT Bhubaneswar has good infrastructure and classrooms. It also has a product design lab, the place where all engineering design comes alive. A total of 89 companies visited the campus at IIT Bhubaneswar in the year 2019. Big core companies like Tata Steel, TCS, L&T, HP, Renault Nissan, Indian oil, and Maruti Suzuki recruited students from the ME department. In the year 2019, 83% of students of ME batch got placed in these companies with an average package of 11.43 LPA. The highest number of jobs was offered by the core sector. PSU like ISRO, IOCL, and NCCBM also participated in the campus placement. The department has several laboratories such as CAD & manufacturing, Robotics & Control, Nanomechanics, and Material science. Institute has also several mechanical related or robotics society which provides an excellent educational experience.